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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 20:42, 27 January 2009
, 20:42, 27 January 2009→Syntactic Transformations: try nested table format
The use of the basic logical connectives can be expressed in the form of a STR as follows:
The use of the basic logical connectives can be expressed in the form of a STR as follows:
<pre>
<br>
If Sj is a sentence
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
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{| align="center" cellpadding="0" cellspacing="0" style="text-align:right" width="100%"
|- style="height:48px"
| width="98%" | <math>\text{Logical Translation Rule 0}\!</math>
| width=2%" |
|}
|-
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:48px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="80%" style="border-top:1px solid black" |
<math>s_j ~\text{is a sentence about things in the universe X}</math>
|- style="height:48px"
|
| <math>\text{and}\!</math>
| <math>p_j ~\text{is a proposition about things in the universe X}</math>
|- style="height:48px"
|
| <math>\text{such that:}\!</math>
|
|- style="height:48px"
|
| <math>\text{L0a.}\!</math>
| <math>\downharpoonleft s_j \downharpoonright ~=~ p_j, ~\text{for all}~ j \in J,</math>
|- style="height:48px"
|
| <math>\text{then}\!</math>
| <math>\text{the following equations are true:}\!</math>
|}
|-
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:56px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\text{L0b.}\!</math>
| width="20%" style="border-top:1px solid black" |
<math>\downharpoonleft \operatorname{Conc}_j^J s_j \downharpoonright</math>
| width="10%" style="border-top:1px solid black" | <math>=\!</math>
| width="20%" style="border-top:1px solid black" |
<math>\operatorname{Conj}_j^J \downharpoonleft s_j \downharpoonright</math>
| width="10%" style="border-top:1px solid black" | <math>=\!</math>
| width="20%" style="border-top:1px solid black" |
<math>\operatorname{Conj}_j^J p_j</math>
|- style="height:56px"
|
| <math>\text{L0c.}\!</math>
| <math>\downharpoonleft \operatorname{Surc}_j^J s_j \downharpoonright</math>
| <math>=\!</math>
| <math>\operatorname{Surj}_j^J \downharpoonleft s_j \downharpoonright</math>
| <math>=\!</math>
| <math>\operatorname{Surj}_j^J p_j</math>
|}
|}
<br>
</pre>
As a general rule, the application of a STR involves the recognition of an antecedent condition and the facilitation of a consequent condition. The antecedent condition is a state whose initial expression presents a match, in a formal sense, to one of the sentences that are listed in the STR, and the consequent condition is achieved by taking its suggestions seriously, in other words, by following its sequence of equivalents and implicants to some other link in its chain.
As a general rule, the application of a STR involves the recognition of an antecedent condition and the facilitation of a consequent condition. The antecedent condition is a state whose initial expression presents a match, in a formal sense, to one of the sentences that are listed in the STR, and the consequent condition is achieved by taking its suggestions seriously, in other words, by following its sequence of equivalents and implicants to some other link in its chain.